On centralizers of reflexive algebras
type: Item
instance of: scholarly article
title: On centralizers of reflexive algebras
zbMATH Open document ID: 1257.47071
author: Jianbin Guo
author: Jiankui Li
published in: Aequationes Mathematicae
publication date: 2012-11-21T00:00:00Z
review text: Let \(\mathcal{L}\) be a subspace lattice on a complex Banach space \(X\) and \(\delta:alg\mathcal{L} \to B(X)\) a linear mapping such that for every \(A \in alg\mathcal{L}\), either \(2\delta(A^2)=\delta(A)A + A\delta(A)\) or \(\delta(A^3) = A\delta(A)A\). In the paper, the authors show that, if \(\vee\{L : L \in \mathcal{J}(\mathcal{L})\}=X\) or \(\wedge\{L_-: L \in \mathcal{J}(\mathcal{L})\}=(0)\) and \(X\) is reflexive, then \(\delta\) is a centralizer. Moreover, the authors prove that, when \(\mathcal{L}\) is a CSL and \(\delta\) is a linear mapping from \(alg\mathcal{L}\) into itself, then \(\delta\) is a centralizer.
Mathematics Subject Classification ID: 47L35
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B60
zbMATH DE Number: 6109270
zbMATH Keywords: CSL algebra
zbMATH Keywords: reflexive algebra
zbMATH Keywords: centralizer
reviewed by: Ajda Fošner
MaRDI profile type: Publication
full work available at URL: s00010-012-0137-y
OpenAlex ID: W2043300906
cites work: A characterization of the centroid of a prime ring
cites work: On Left Derivations and Related Mappings
cites work: Jordan Derivations on Rings
cites work: Q3994569
cites work: Q5325481
cites work: An equation related to two-sided centralizers in prime rings.
cites work: On some functional equations arising from \((m,n)\)-Jordan derivations and commutativity of prime rings.
cites work: Identities with generalized derivations in prime rings.
cites work: Jordan Derivations of Prime Rings
cites work: On centralizers of standard operator algebras and semisimple \(H^*\)-algebras
cites work: Jordan derivations of reflexive algebras
cites work: The Jordan structure of CSL algebras
cites work: On the rank of operators in reflexive algebras
cites work: Operators of Rank One in Reflexive Algebras
cites work: Strongly Reflexive Lattices
cites work: On certain functional equation arising from \((m,n)\)-Jordan centralizers in prime rings.
cites work: Q4799926
cites work: Q4828846
cites work: Identities related to derivations and centralizers on standard operators algebras
cites work: On left Jordan derivations of rings and Banach algebras
cites work: On (m,n)-Jordan centralizers in rings and algebras
cites work: Q3015299
cites work: A characterization of two-sided centralizers on prime rings.
cites work: Q3544340
cites work: Centralisers on rings and algebras
cites work: Q3989696
DOI: 10.1007/S00010-012-0137-Y
description: scientific article; zbMATH DE number 6109270